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Research Article | Open Access

Some dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus

Elkhateeb S. Aly1, Y. A. Madani2, F. Gassem2, A. I. Saied3, H. M. Rezk4, Wael W. Mohammed2,5( )
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Abstract

In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse H ölder's inequality, integration by parts, and chain rule on time scales nabla calculus. As special cases of our results (when T = R ), we get the continuous analouges of inequalities proven by Benaissa and Sarikaya, and when T = N 0 , the results to the best of the authors' knowledge are essentially new.

Keywords

Hardy-type inequalities with negative parameterstime scalesreverse Hölder's inequalitychain rule
CLC number: 26D10, 26D15, 34N05, 47B38, 39A12

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 5147-5170
DOI: 10.3934/math.2024250

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Cite this article:
Aly ES, Madani YA, Gassem F, et al. Some dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus. AIMS Mathematics, 2024, 9(2): 5147-5170. https://doi.org/10.3934/math.2024250

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Received: 13 December 2023
Revised: 08 January 2024
Accepted: 19 January 2024
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)